kulupu pi ken nanpa

kulupu pi ken nanpa li ni: ona li jo e ijo pi pini ala. taso jan li ken pana e nanpa ante pi nanpa ijo tawa e ijo ale lon kulupu.

kulupu pi ken nanpa

jan li ken lukin pona e ni: nanpa pi wan nanpa la, ni li ken:

• 1 - 0
• 2 - 1
• 3 - -1
• 4 - 2
• 5 - -2
• ...

kulupu pi nanpa kipisi ale ($\mathbb {Q}$) li kulupu pi ken nanpa kin. pana nanpa la, pali li ni:

• kulupu e ona kepeken wan pi nanpa lawa pi mute kipisi:
  • 2: 1/1
  • 3: 1/2, 2/1
  • 4: 1/3, 2/2, 3/1
• nanpa li ken kama lili la, o weka e ona: 2/2 li sama 1/1.
• kulupu ni ale li jo e ijo pi nanpa pini. ni la, sina ken nanpa e kulupu nanpa wan e kulupu nanpa tu e kulupu ale kepeken nasin sama: 1/1, 1/2, 2/1, 1/3, 3/1, ...

kulupu pi ken nanpa ala

kulupu pi nanpa ma ale ($\mathbb {R}$) la, nasin ala li nanpa e ona. jan Keko Kanto (Georg Kantor) li kama sona e ni kepeken nasin ni: ona li lukin taso e nanpa lon insa pi kipisi (0,1). jan li ken sitelen e ona kepeken nanpa 0, 1, ... 9 pi pini ala: 0,6535753280160... jan li jo e nasin nanpa la, nanpa li lon insa ala:

ni li nanpa pi nasin nanpa:

$z_{1}=0,{\underline {a_{11}}}\ a_{12}\ a_{13}\ldots$

$z_{2}=0,a_{21}\ {\underline {a_{22}}}\ a_{23}\ldots$

$z_{3}=0,a_{31}\ a_{32}\ {\underline {a_{33}}}\ldots$

$z_{4}=\ldots$

$\vdots$

o kepeken wan nanpa pi linja anpa: $0,a_{11},a_{22},a_{33},\ldots$. nanpa ni en nanpa ale pi nasin nanpa li jo e wan sama. ona la, o ante e wan ale. nanpa li kama tan pali ni la, ona en nanpa ale pi nasin nanpa li jo e wan pi sama ala. ni la, ona li lon insa ala pi nasin nanpa.

sama la, ni li kulupu pi ken nanpa ala: ona li jo e kulupu ale lon insa kulupu pi ken nanpa. ken la, nanpa pi nanpa ijo la, ona li jo e kulupu ona ale. o lukin e ni tan ni: nanpa lon insa (0,1) la, jan li ken sitelen e ona kepeken 0 kepeken 1 taso (sama lon insa pi ilo kon, taso kepeken wan pi pini ala). wan nanpa wan la, 1 li pana sona e ni: nanpa 1 li lon insa kulupu. 0 li pana sona e ni: nanpa 1 li lon insa kulupu ala. wan nanpa tu li pana e sona sama lon nanpa 2. o lukin e nanpa ante ale kepeken nasin sama. ni la pali sama pi pali lon sewi.

suli kulupu mute

kulupu pi ken nanpa ala li suli sama lon ni: jan li ken pana e ijo pi kulupu wan lon poka ijo pi kulupu ante. ijo wan taso o lon poka ijo wan taso. ni la, kulupu pi nanpa ma en kulupu pi nanpa nasa li suli sama:

o sitelen e nanpa kepeken nanpa 0, 1, ... 9. nanpa nasa la, o sitelen e wan pi nanpa ma e wan pi nanpa kon kepeken nasin sama ilo wan len pi nena lili: 123,4567+8,98765i -> 102038,4958677605.

taso sama pana sona lon sewi la, kulupu pi nanpa ma ale li lili lon poka kulupu ni: ona li jo e kulupu ale pi nanpa ma.